For atoms with two or more electrons, the governing equations can only be solved with the use of methods of iterative approximation.

For example, the allotropes of carbon include diamond ( where the carbon atoms are bonded together in a tetrahedral lattice arrangement ), graphite ( where the carbon atoms are bonded together in sheets of a hexagonal lattice ), graphene ( single sheets of graphite ), and fullerenes ( where the carbon atoms are bonded together in spherical, tubular, or ellipsoidal formations ).

For example, all atoms with 6 protons in their nuclei are atoms of the chemical element carbon, and all atoms with 92 protons in their nuclei are atoms of the element uranium.

For example, water is a compound containing hydrogen and oxygen in the ratio of two to one, with the oxygen atom between the two hydrogen atoms, and an angle of 104. 5 ° between them.

For example, all carbon atoms contain 6 protons in their nucleus ; so the atomic number of carbon is 6.

For example, carbon can be found as diamond, which has a tetrahedral structure around each carbon atom ; graphite, which has layers of carbon atoms with a hexagonal structure stacked on top of each other ; graphene, which is a single layer of graphite that is incredibly strong ; fullerenes, which have nearly spherical shapes ; and carbon nanotubes, which are tubes with a hexagonal structure ( even these may differ from each other in electrical properties ).

For example, trace ( but detectable ) amounts of carbon-14 (< sup > 14 </ sup > C ) are continually produced in the atmosphere by cosmic rays impacting nitrogen atoms, and argon-40 (< sup > 40 </ sup > Ar ) is continually produced by the decay of primordially occurring but unstable potassium-40 (< sup > 40 </ sup > K ).

For the study of the mechanical behavior of solids and fluids these are assumed to be continuous bodies, which means that the matter fills the entire region of space it occupies, despite the fact that matter is made of atoms, has voids, and is discrete.

For example, a perfect crystal of diamond would only contain carbon atoms, but a real crystal might perhaps contain a few boron atoms as well.

For example, some alloys have a regular structure in which every other atom is a different species ; for illustration assume that type A atoms sit on the corners of a cubic lattice, and type B atoms sit in the center of the cubes.

For instance, in a perfect sheet of graphite ( graphene ) all atoms are in rings containing six atoms.

For instance, in ideally bonded amorphous silica all Si atoms have 4 bonds to O atoms and all O atoms have 2 bonds to Si atom.

For instance, dark bands in the light emitted by a distant star are due to the atoms in the star's atmosphere.

For instance, when atoms are irradiated by a source with a broad spectrum, distinct absorption lines will appear in the spectrum of transmitted radiation.

For example, an allyl group can coordinate to palladium in the η¹ mode ( only one atom of an allyl group attached to palladium ) or the η³ mode ( 3 atoms attached to palladium ).

For small business, basic client service can be accomplished by a contact manager system: an integrated solution that lets organizations and individuals efficiently track and record interactions, including emails, documents, jobs, faxes, scheduling, and more.

; Automated optimization: For frequently occurring usage patterns or requests, some DBMS can adjust themselves to improve the speed of those interactions.

For that reason in some cases cult leader's pictures were burned or there were highly confrontational interactions between deprogrammers and cultist.

For example, the identity of proteins of the immune system ( e. g. antibodies ), and the mechanism by which they recognize and bind to foreign antigens would remain very obscure if not for the extensive use of in vitro work to isolate the proteins, identify the cells and genes that produce them, study the physical properties of their interaction with antigens, and identify how those interactions lead to cellular signals that activate other components of the immune system.

For example, asteroids of the Alinda family are in or close to the 3: 1 resonance, with their orbital eccentricity steadily increased by interactions with Jupiter until they eventually have a close encounter with an inner planet that ejects them from the resonance.

For example, synthetic peptides can be used as probes to see where protein-peptide interactions occur-see the page on Protein tags.

* For overviews, see Standard Model, its field theoretical formulation, strong interactions, quarks and gluons, hadrons, confinement, QCD matter, or quark-gluon plasma.

For example, the possible interactions between groups of molecules grows enormously with the number of molecules such that it is impossible for a computer to even list the arrangements for a system as small as 20 molecules.

For instance, the laws of thermodynamics are remarkably simple, even if the laws which govern the interactions between component particles are complex.

For such reasons, some industrial UPS management systems recommend periodic replacement of entire battery arrays potentially using hundreds of expensive batteries, due to these damaging interactions between new batteries and old batteries, within and across series and parallel strings.

For example, mutualistic interactions are vital for terrestrial ecosystem function as more than 48 % of land plants rely on mycorrhizal relationships with fungi to provide them with inorganic compounds and trace elements.

For example, chimpanzees, which are continuous breeders, show significantly raised testosterone levels and aggressive male-male interactions when receptive and fertile females are present.

For two loci, 14 classes of epistatic interactions are recognized.

For physical problems involving interactions between particles,

For example, biologists studying stress in fish showed that social subordination leads to chronic stress, related to reduced aggressive interactions, to lack of control, and to the constant threat imposed by dominant fish.

For bosonic particles that exhibit rest mass when they are free and " real ," virtual interactions are characterized by the relatively short range of the force interaction produced by particle exchange.

For example, when an antigen presenting cell expresses an antigen on MHC class II, a CD4 < sup >+</ sup > cell will aid those cells through a combination of cell to cell interactions ( e. g. CD40 and CD40L ) and through cytokines.

For the testing phase, the script was broken into small segments, each comprising only one or two interactions.

For a suitable combination of negative ( anomalous ) net GDD with the Kerr nonlinearity, soliton-like interactions may stabilize the mode-locking and help to generate shorter pulses.

For example, Arg 218 has electrostatic interactions with other nearby residues, restricting oxyluciferin from tautomerizing to the enol form.

For all methods of legal fishing for toothfish, there are minimal interactions with seabirds these days.

For example, using Hamilton's broad based inclusive fitness model ( Hamilton 1964 a, b ), Robert Trivers ' in Social Evolution ( Trivers 1985 ) has outlined how a selfish gene can maximize its inclusive fitness, spreading copies of itself via interactions that lead solely to selfishness, or to mutualism with unrelated individuals, or to delayed reciprocity, a highly specialized reciprocity that can involve both kin and non-kin that is subject to cheating and remembering cheaters, or to facultative altruism and obligate altruism with kin.

For example, Jaak Panksepp, an affective neuroscientist, point to the " remarkable degree of neocortical plasticity within the human brain, especially during development " and states that " the developmental interactions among ancient special-purpose circuits and more recent general-purpose brain mechanisms can generate many of the ‘ modularized ’ human abilities that evolutionary psychology has entertained.

For cosmic gamma-ray events, the experiment required two nearly simultaneous interactions, in a set of front and rear scintillators.

For his part, Thompson had explained in a previous letter that there would be nothing but an honorable friendship between Katie and himself.

For some time the Communists honored the distinction between the Soviet zone of Germany and the Soviet sector of Berlin by promulgating separately the laws for the two areas.

For the States which maintain two separate agencies -- one for the vocational rehabilitation of the blind, and one for the rehabilitation of persons other than the blind -- the Act specifies that their minimum ( base ) allotment shall be divided between the two agencies in the same proportion as it was divided in fiscal year 1954.

For four of the six ( the anaconda and the amethystine python cannot be included for lack of data ) there is also a correlation between size at maturity and maximum length, the boa constrictor being the smallest and the Indian python the next in size at the former stage.

For some forms of philosophy, this very division between the empirical and the rational becomes a sign of the metaphysical superiority of the latter.

For the illusion of depth created by the contrast between the affixed material and everything else gives way immediately to an illusion of forms in bas-relief, which gives way in turn, and with equal immediacy, to an illusion that seems to contain both -- or neither.

For the convenience of guests bundle centers have been established throughout the city and suburbs where the donations may be deposited between now and the date of the big event.

For example, the 2nd Academy Awards presented on April 3, 1930, recognized films that were released between August 1, 1928 and July 31, 1929.

For example, the randomization-based analysis results in a small but ( strictly ) negative correlation between the observations.

** Tarski's theorem: For every infinite set A, there is a bijective map between the sets A and A × A.

For such an online algorithm, a recurrence relation is required between quantities from which the required statistics can be calculated in a numerically stable fashion.

For blacklip abalone, the size limit varies from between 138 mm for the southern end of the state and 127 mm for the northern end of the state.

For example, the main crossover of the Andes between Argentina and Chile is still accomplished through the Paso Internacional Los Libertadores.

For example, if the water is 25 ft ( 8 m ) deep, and the anchor roller is 3 ft ( 1 m ) above the water, the scope is the ratio between the amount of cable let out and 28 ft ( 9 m ).

For the first time a conceptual and procedural distinction was made between laws and decrees.

For instance, antibacterial resistance genes can be exchanged between different bacterial strains or species via plasmids that carry these resistance genes.

For very large distances, cosmological redshift complicates the relation between absolute and apparent magnitude, and an additional k correction might be required.

For Friedrich Wilhelm Joseph Schelling, the philosophy of art is the " organon " of philosophy concerning the relation between man and nature.

For some, aesthetics is considered a synonym for the philosophy of art since Hegel, while others insist that there is a significant distinction between these closely related fields.

For according to them, there were seven islands in that sea in their time, sacred to Persephone, and also three others of enormous size, one of which was sacred to Hades, another to Ammon, and another one between them to Poseidon, the extent of which was a thousand stadia ; and the inhabitants of it — they add — preserved the remembrance from their ancestors of the immeasurably large island of Atlantis which had really existed there and which for many ages had reigned over all islands in the Atlantic sea and which itself had like-wise been sacred to Poseidon.

For example, using Cartesian coordinates on the plane, the distance between two points ( x < sub > 1 </ sub >, y < sub > 1 </ sub >) and ( x < sub > 2 </ sub >, y < sub > 2 </ sub >) is defined by the formula

( For the famous relationship between Mozart and Salieri please see below.

For example between 1985 and 1989, 5, 000 civilians were killed in fighting between the two parties.

For example, the Barony of Grey of Codnor was in abeyance for over 490 years between 1496 and 1989, and the Barony of Hastings was similarly in abeyance for over 299 years from 1542 to 1841.